2024-06-19T04:49:56Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00011969
2023-01-16T04:42:32Z
697:698:699
Zeta and L-functions and Bernoulli polynomials of root systems
Komori, Yasushi
Matsumoto, Kohji
Tsumura, Hirofumi
open access
Multiple zeta-function
Witten zeta-function
root systems
simple Lie
algerasanalytic continuation
functional relation
This article is essentially an announcement of the papers [7,8,9,10] of the authors, though some of the examples are not included in those papers. We consider what is called zeta and L-functions of root systems which can be regarded as a multi-variable version of Witten multiple zeta and L-functions. Furthermore, corresponding to these functions, Bernoulli polynomials of root systems are defined. First we state several analytic properties, such as analytic continuation and location of singularities of these functions. Secondly we generalize the Bernoulli polynomials and give some expressions of values of zeta and L-functions of root systems in terms of these polynomials. Finally we give some functional relations among them by our previous method. These relations include the known formulas for their special values formulated by Zagier based on Wittenâ€™s work.
Japan Academy
2008
eng
journal article
VoR
http://hdl.handle.net/2237/13843
https://nagoya.repo.nii.ac.jp/records/11969
Proceedings of the Japan Academy, Ser. A Mathematical Sciences
84
5
57
62
https://nagoya.repo.nii.ac.jp/record/11969/files/proc_japan_acad_84.pdf
application/pdf
131.9 kB
2018-02-20